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The Maxima on-line user's manual

Algebra Calculator

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Pochhammer Calculator

Pochhammer

Function: pochhammer (<n>, <x>) The Pochhammer symbol. For nonnegative integers <n> with <n> <= pochhammer_max_index, the expression pochhammer (<x>, <n>) evaluates to the product <x> (<x> + 1) (<x> + 2) ... (<x> + n - 1) when <n> > 0 and to 1 when <n> = 0. For negative <n>, pochhammer (<x>, <n>) is defined as (-1)^<n> / pochhammer (1 - <x>, -<n>). Thus

pochhammer (4/3, 2);
 pochhammer (4/3, 3);
 pochhammer (4/3, 4);
 pochhammer (4/3, 5);

          (%i1) pochhammer (x, 3);
          (%o1)                   x (x + 1) (x + 2)
          (%i2) pochhammer (x, -3);
                                           1
          (%o2)               - -----------------------
                                (1 - x) (2 - x) (3 - x)

To convert a Pochhammer symbol into a quotient of gamma functions, (see Abramowitz and Stegun, equation 6.1.22) use makegamma; for example

          (%i1) makegamma (pochhammer (x, n));
                                    gamma(x + n)
          (%o1)                     ------------
                                      gamma(x)

When <n> exceeds pochhammer_max_index or when <n> is symbolic, pochhammer returns a noun form.

          (%i1) pochhammer (x, n);
          (%o1)                         (x)
                                           n

There are also some inexact matches for pochhammer. Try ?? pochhammer to see them.

(%o1)                                true
(%i2) 

Pochhammer Example

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